Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.ci
\(\chi_{4029}(185,\cdot)\) \(\chi_{4029}(308,\cdot)\) \(\chi_{4029}(410,\cdot)\) \(\chi_{4029}(491,\cdot)\) \(\chi_{4029}(614,\cdot)\) \(\chi_{4029}(644,\cdot)\) \(\chi_{4029}(665,\cdot)\) \(\chi_{4029}(689,\cdot)\) \(\chi_{4029}(848,\cdot)\) \(\chi_{4029}(926,\cdot)\) \(\chi_{4029}(1175,\cdot)\) \(\chi_{4029}(1199,\cdot)\) \(\chi_{4029}(1226,\cdot)\) \(\chi_{4029}(1256,\cdot)\) \(\chi_{4029}(1358,\cdot)\) \(\chi_{4029}(1436,\cdot)\) \(\chi_{4029}(1562,\cdot)\) \(\chi_{4029}(1607,\cdot)\) \(\chi_{4029}(1613,\cdot)\) \(\chi_{4029}(1844,\cdot)\) \(\chi_{4029}(1913,\cdot)\) \(\chi_{4029}(2066,\cdot)\) \(\chi_{4029}(2123,\cdot)\) \(\chi_{4029}(2150,\cdot)\) \(\chi_{4029}(2174,\cdot)\) \(\chi_{4029}(2270,\cdot)\) \(\chi_{4029}(2303,\cdot)\) \(\chi_{4029}(2348,\cdot)\) \(\chi_{4029}(2507,\cdot)\) \(\chi_{4029}(2678,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{104})$ |
Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{5}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(2270, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{59}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{61}{104}\right)\) | \(e\left(\frac{1}{13}\right)\) |